Voltage and current reference circuits find many applications in electronic circuit applications. The bandgap reference circuit is a common circuit solution for supplying a voltage or current reference. FIG. 1 is a prior art bandgap circuit 10 and operates as described in "New Developments in IC Voltage Regulators", Widlar, Robert J., IEEE Journal of Solid State Circuits, Vol. sc-6, No. 1, Feb. 1971. M1 and M2 act as a standard MOS current mirror providing current to Q1 and Q2 which are configured as a bipolar current mirror. Q1 and Q2 are sized differently; therefore, although they conduct the same current, they have different current densities. Therefore, there will be a difference in their V.sub.bc voltages and the difference will be reflected in the current through R1. V.sub.out is a voltage reference that is a function of the current through R2 and the base-emitter voltage V.sub.be of Q3. Since the current through R2 is mirrored from M2 it is seen that the current through M3 is a function of .DELTA.V.sub.be between Q1 and Q2 and R1. Therefore, V.sub.out is a function of the .DELTA.V.sub.bc between Q1 and Q2, the ratio in resistor values R1 and R2, and V.sub.be of Q3 as seen below: EQU V.sub.out =I(M3)*R2+V.sub.be (Q3)
and, EQU I(M3)=I(M2)=I.sub.c (Q2).apprxeq.I.sub.c (Q2)=.DELTA.V.sub.be /R1
where EQU .DELTA.V.sub.be =V.sub.be (Q2)-V.sub.be (Q1).
Substituting .DELTA.V.sub.be /R1 for I(M3) you get EQU V.sub.out =(R2R1)*.DELTA.V.sub.be +V.sub.be (Q3).
If the ratios of R1 and R2 are set appropriately V.sub.out will have zero temperature coefficient. This ratio is determined by taking the equation for V.sub.out that incorporates all temperature dependencies, differentiating with respect to temperature, and setting the equation equal to zero. This is well known by those skilled in the art of bandgap reference circuits. The above explanation of prior art circuit 10 assumes that the gain (or h.sub.FE) of Q1 and Q2 are sufficiently high such that I.sub.c (Q2) is approximately I.sub.c (Q2). However, in many cases, this is not a valid assumption. In integrated circuits, h.sub.FE mary vary by an order of magnitude for a given process. Additionally, h.sub.FE is a strong function of temperature and may increase by 4.times.from -55.degree. C. to 125.degree. C. Taking into account low h.sub.FE, the following equations represent circuit 10: EQU V.sub.out =I(M3)*R2+V.sub.be (Q3)
and, EQU I(M3)=I(M2)=I.sub.c (Q2)
and, EQU I.sub.c (Q2)=I.sub.c (Q2)-I.sub.b (Q2)
therefore, EQU I.sub.c (Q2)=.DELTA.V.sub.be /R1-I.sub.b (Q2)
and, EQU V.sub.out =(R2/R1)*.DELTA.V.sub.be +V.sub.be (Q3)-R2*I.sub.b (Q2).
Therefore, it can be seen that an error term exists and further, this error term is a function of temperature since I.sub.b (Q2) will vary as h.sub.FE varies over temperature. This error term deteriorates the performance of circuit 10 as a voltage reference.
FIG. 2 is a prior art bandgap circuit 20 that incorporates an NMOS transistor M4 as a "beta-helper" and is well known by those skilled in the art. M4 decreases the dependance upon beta (h.sub.FE) to achieve accurate "mirroring" of current between Q1 and Q2 by minimizing the current needed from the collector terminal of Q1 to supply base drive to Q1 and Q2. Although M4 is effective in that regard it does not eliminate the error term in V.sub.out associated with a low h.sub.Fe in Q2.
The same error phenomena is also present in bandgap current reference circuits. That is, when bipolar transistors exhibit low gain there is a significant current difference between their collector current and their emitter current. Since the emitter current is what is used to establish the current reference stabilization, a difference between the collector current and emitter current due to low gain causes significant error in establishing a stable current reference.
It is an object of this invention to provide a compensation method and circuit that reduces the negative effect of low gain bipolar transistors in bandgap voltage and current reference circuits. Other objects and advantages of the invention will become apparent to those of ordinary skill in the art having reference to the following specification together with the drawings herein.